A note on the eigenvalues of \(g\)-circulants (and of \(g\)-Toeplitz, \(g\)-Hankel matrices)
type: Item
instance of: scholarly article
title: A note on the eigenvalues of \(g\)-circulants (and of \(g\)-Toeplitz, \(g\)-Hankel matrices)
zbMATH Open document ID: 1312.15013
author: Debora Sesana
author: Stefano Serra Capizzano
published in: Calcolo
publication date: 2015-03-23T00:00:00Z
review text: A \(g\)-circulant matrix \(A\) of size \(n\times n\) is of the form \(A=[a_{(r-gs)\,\text{mod}\, n}]_{r,s=0}^{n-1}\), while a matrix \(A\) is called \(g\)-Toeplitz if \(A=[a_{r-gs}]_{r,s=0}^{n-1}\). The paper mainly studies the eigenvalues of \(g\)-circulants and eigenvalue distribution of \(g\)-Teoplitz sequence. Closed form expressions of the eigenvalues of \(g\)-circulants are provided. If the entries \(a_k\) are Fourier coefficients of an integrable funcion \(f\) over the domain \((-\pi, \pi)\), a preliminary analysis of the spectral distribution of \(g\)-Toeplitz sequence is considered and the results are given in Theorem 5.1 and 5.2. A conjecture is given.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15B05
zbMATH DE Number: 6418693
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: Hankel matrix
zbMATH Keywords: spectral distributions
zbMATH Keywords: multigrid methods
zbMATH Keywords: \(g\)-circulant matrix
zbMATH Keywords: eigenvalue
reviewed by: Tin-Yau Tam
MaRDI profile type: Publication
full work available at URL: s10092-013-0104-6
OpenAlex ID: W2025758805
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DOI: 10.1007/S10092-013-0104-6
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description: scientific article; zbMATH DE number 6418693